Grating structure for directing non-polarized light

ABSTRACT

A grating structure having a fused silica base includes alternating ridges and grooves. The ridges and grooves form a fused silica to air interface. The ridges and grooves are configured such that the grating has a ratio between the effective refractive index difference between s-polarization and p-polarization of about 1/3. As such, for non-polarized light with an incident angle θ in  of between 40° and 90° and a wavelength λ=350-1600 nm, the grating directs both s-polarization and p-polarization components of the incident light to the −1 st  order diffraction mode.

BACKGROUND

1. Field of the Invention

The present invention generally relates to a grating structure.

2. Description of Related Art

Various grating structures have been introduced in industry. Gratingstypically have rows of grating lines that diffract light. The diffractedlight is generally distributed into a diffraction pattern forming anumber of modes. One type of diffraction grating is a transmissiongrating. Typically, transmission gratings comprise grooves etched into atransparent material. As the elements of light in the incident spectrumstrike the grooves at a certain angle, they are diffracted and,therefore, separated to various degrees. In many optical applications,light sources generate diffuse light with randomized polarizations. Inthese applications, typical gratings waste much of the light and,therefore, are not efficient in many beam conditioning applications.

In view of the above, it is apparent that there exists a need for animproved grating structure.

SUMMARY

In satisfying the above need, as well as overcoming the enumerateddrawbacks and other limitations of the related art, the presentinvention provides an improved grating structure.

In one configuration, the grating structure has a fused silica base. Thefused silica base includes alternating ridges and grooves that may beetched into the base. The ridges and grooves form a fused silica to airinterface. The ridges and grooves are configured such that the gratinghas a ratio of the effective refractive index difference betweens-polarization and p-polarization of about 1/3. As such, fornon-polarized light with an incident angle θ_(in) of between 40° and 90°and a wavelength λ=350-1600 nm the grating directs both s-polarizationand p-polarization components of incident light to the −1^(st) orderdiffraction mode.

Further objects, features and advantages of this invention will becomereadily apparent to persons skilled in the art after a review of thefollowing description, with reference to the drawings and claims thatare appended to and form a part of this specification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view of a transmission grating;

FIG. 2 is a perspective view of a transmission grating;

FIG. 3 is a flow chart illustrating a method for producing a grating;

FIGS. 4 a and 4 b are a graphs illustrating the relationship of theeffective refractive index difference between p-polarized light ands-polarized light relative to the fill factor of the grating;

FIG. 5 a is a graph illustrating the relationship of the effectiverefractive index difference relative to angle of incidence;

FIG. 5 b is a graph illustrating the relationship of the height relativeto angle of incidence;

FIG. 5 c is a graph illustrating the relationship of the fill factorrelative to angle of incidence;

FIG. 5 d is a graph illustrating the relationship of the aspect ratiorelative to angle of incidence;

FIGS. 6 a and 6 b are a graphs illustrating the relationship of thediffraction efficiency relative to the height of the grating;

FIG. 7 is a graph illustrating the relationship of the diffractionefficiency relative to the angle of incidence;

FIG. 8 is a sideview of a tail light assembly including a transmissiongrating; and

FIGS. 9 a and 9 b are graphs illustrating the relationship of thediffraction efficiency relative to the change in incident angle andnormalized wavelength.

DETAILED DESCRIPTION

Referring to FIG. 1, a system 10 including a transmission grating 11 isprovided. The transmission grating 11 may be a fused silica transmissiongrating with a silica to air interface. As such, air surrounds a silicastructure 12 and is denoted by reference number 14. The silica structure12 includes a base 16 of solid fused silica. Fused silica is verytransparent and transmits a very broad bandwidth of light. Further,fused silica offers a very stable material that can be used over a widerange of temperature conditions. In addition, fused silica gratings maybe easily etched to provide the grating properties required for manyapplications. Fused silica has an index of refraction of about 1.45 incontrast to air with an index of refraction of about 1. The symbol n_(α)is used to denote the refraction index of air and n_(β) is used todenote the refraction index for fused silica.

Protrusions 18 extend from and are integral with the base 16. Beingintegral with the base 16 the protrusions 18 are also formed of fusedsilica. The protrusions 18 form grooves 20 located between eachprotrusion 18. The grooves 20 may be filled with air 14, therebyproviding an air fused silica interface across the grating layer 22. Thegrating layer 22 diffracts light directed towards the transmissiongrating 11 from a light source into various diffraction modes. Each ofthe protrusions 18 may form a ridge 38 that extends to provide a uniformline structure, as denoted by lines 40 in FIG. 2. The protrusions 18 mayhave a top surface 42 and side surfaces 44. The side surfaces 44 mayhave various profiles or may be substantially straight.

Referring again to FIG. 1, incident light may be provided to thetransmission grating 11, as denoted by arrow 30. The incident light 30has an incident angle θ_(in) relative to the principle axis 31 of thegrating projections 18. In addition, the incident light 30 may comprisevarious light polarizations. For example, the incident light maycomprise components that are s-polarized 30A and components that arep-polarized 30B. S-polarization denotes when the electrical field isperpendicular to the plane of light propagation. P-polarization denoteswhere the electrical field is parallel to the plane of lightpropagation. When the incident light 30 interacts with the grating layer22, the incident light 30 will form reflective components denoted by Rand transmissive components denoted by T.

The reflective components may form a diffraction pattern comprised of aplurality of modes. For example, the 0 order mode of the reflectivecomponent R_(n=0) is denoted by arrow 32. Similarly, the −1^(st) ordermode of the reflective component R_(n=−1) is denoted by arrow 34. Inaddition, the transmission grating 11 is mounted in the Littrow mountingcondition. Littrow mounting is the condition that produces the sameangle of diffraction for both the −1^(st) and 0^(th) order modes, but inopposite directions. The angle for the −1^(st) order mode is θ_(r,−1),while the angle for the 0^(th) order mode is θ_(r,0).

The transmissive components may also form a diffraction patterncomprised of a plurality of modes. For example, the 0 order mode of thetransmissive component T_(n=0) is denoted by arrow 36. Similarly, the−1^(st) order mode of the transmissive component T_(n=−1) is denoted byline 38. Again, the Littrow mounting produces the same angle ofdiffraction for both the −1^(st) and 0^(th) order modes, but in oppositedirections. The angle for the −1^(st) order mode is θ_(t,−1), while theangle for the 0^(th) order mode is θ_(t,0).

The resulting characteristics of the reflective and transmissivecomponents are a factor of the refractive index (n) of the material, theperiod (p) of the grating, the fill factor (r) of the grating, and theheight (h) of the grating. The period of the grating is the distancefrom the start of one groove to the start of the next groove. The periodof the transmission grating 11 is denoted by reference numeral 24. Thefill factor (r) can be defined as the ratio of the protrusion width orgroove width to the period of the grating, which is denoted by referencenumeral 26. The height (h) of the grating is the distance from the topof the protrusion 18 to the bottom of the groove 20, which is denoted byreference numeral 28 in FIG. 1. As one would readily understand, thegrooves 20 and protrusions 18 may not form exact right angles andvarious profiles may be used along the edge 42 of the protrusions 18. Assuch, the calculation for the fill factor (r) or grating height (h) maybe slightly modified depending on the shape of the projections 18 andgrooves 20. As such, these values may be determined based on the centerof gravity of the projections 18 and grooves 20.

A Littrow mounting condition of the transmission grating 11 having aninterface of air/fused silica may be analyzed by modal analysis, and canbe derived to provide simultaneously a −1st order diffraction for bothp-polarization and s-polarization. The analysis points out that theeffective refractive index difference of two propagation modes in thegrating has a ratio of 1/3 with an incident angle above 40° to selectthe minimum aspect ratio of the groove height to the ridge width orgroove height to groove width. The grating structure fulfilling thiscondition exhibits a transmittance of more than 90% and an aspect ratiofrom 6.6 to 16.8 free space wavelengths for an incident angle from 30°to 50°. A 90° coupler is presented as one application for incoherentlight.

With regard to analysis methods, rigorous coupled-wave analysis has anadvantage of accommodating various groove shapes. Several shapes ofgrooves such as semi-circle, rectangular, triangular, and curvedsurfaces can be used. Coupled-wave analysis is typically used fordesigning gratings, but due to various assumptions this method would notidentify the described parameters. Coupled-wave analysis is a numericalanalysis and does anticipate propagation mode and evanescent modeintegration. On the other hand, a modal analysis can provide a physicalinsight of diffraction phenomena, although it has less flexibility toadapt for various groove shapes.

When gratings are used for unpolarized light such as light emittingdiodes (LEDs), both p-polarization and s-polarization should besimultaneously taken into account in the design. Particularly, the useof −1st order diffraction extends the design degrees of freedom foroptical devices, components, and assembled systems due to large bendingof light. P-polarization and s-polarized −1st order diffraction can beachieved with incident angle from 30° to 45° by computer optimizationusing coupled-wave analysis. However, it was thought that a gratingneeded a larger height and ridge width to accommodate increasingincident angles.

However according to the method described herein, a Littrow mountingcondition of rectangular grating at the interface of air/fused silicamay be derived through a modal analysis to provide simultaneously a −1storder diffraction for both p-polarization and s-polarization. Theanalysis can identify that the ratio of the effective refractive indexdifference of two propagation modes in the grating for p-polarizationand s-polarization depends on incident angle, resulting in differentratios to select the minimum aspect ratio of the grating height to theridge width of fused silica or the groove width of air.

In the modal analysis, effective index, n_(eff), of excited modes in thegrating satisfies the eigenvalue equation.

$\begin{matrix}{{{{{\cos\left( {\beta\;{rp}} \right)}{\cos\left( {{\alpha\left( {1 - r} \right)}p} \right)}} - {\frac{1}{2}\left( {\frac{\alpha\; t_{\alpha}}{\beta\; t_{\beta}} + \frac{\beta\; t_{\beta}}{\alpha\; t_{\alpha}}} \right){\sin\left( {\beta\;{rp}} \right)}{\sin\left( {{\alpha\left( {1 - r} \right)}p} \right)}}} = {\cos\left( {{kn}_{\alpha}p\;{\sin\left( \theta_{in} \right)}} \right)}}\mspace{79mu}{where}} & (1) \\{\mspace{79mu}{\alpha = \sqrt{\left( {kn}_{\alpha} \right)^{2} - n_{eff}^{2}}}} & \left( {2a} \right) \\{\mspace{79mu}{\beta = \sqrt{\left( {kn}_{\beta} \right)^{2} - n_{eff}^{2}}}} & \left( {2b} \right) \\{\mspace{79mu}{t_{\alpha} = \left\{ \begin{matrix}ɛ_{\alpha} & \left( {p - {{pol}.}} \right) \\1 & \left( {s - {{pol}.}} \right)\end{matrix} \right.}} & \left( {3a} \right) \\{\mspace{79mu}{t_{\beta} = \left\{ \begin{matrix}ɛ_{\beta} & \left( {p - {{pol}.}} \right) \\1 & \left( {s - {{pol}.}} \right)\end{matrix} \right.}} & \left( {3b} \right)\end{matrix}$

α, β, and t are parameters in equation (1), and defined by equations(2a)-(3b), k is the wave number, and ε_(α) and ε_(β) are permittivity ofair and fused silica. In Littrow mounting, the right part of equation(1) equals minus unity. Excited modes are numbered from the largestvalue of the square of the effective refractive index, n_(eef) ². Withinan incident angle θ_(in) from 30° to 90°, the lowest two modes, m=0 and1, are propagation modes with positive n_(eef) ², while other modes,m≧2, are evanescent modes with negative n_(eef) ². Here, m=0 and 1 areconsidered with an incident angle θ_(in) from 30° to 85°. Also, thegrating may provide the highest diffraction efficiency with the −1storder when the grating height, h, is set so as to have a phasedifference of 180° between the lowest two modes, satisfying equations(4a), (4b).

$\begin{matrix}{n_{d} = \frac{\lambda}{2h}} & \left( {4a} \right)\end{matrix}$where effective refractive index difference, n_(d), is written withn _(d) =n _(m=0) −n _(m=1)  (4b)where λ is free space wavelength, and n_(m=0) and n_(m=1) are effectiverefractive index of modes m=0 and 1.

A method for producing a grating according to one embodiment is providedin process 300. In block 310, the wavelength range of light is defined.In block 312, the incident angle of the light is defined. In block 314,the period of the grating is defined based on a Littrow mountingcondition. In block 316, the relationship between the effectiverefractive index difference and the fill factor is determined. effectiverefractive index difference can be graphed with respect to the fillfactor for both s-polarization and p-polarization, as shown in the graphin FIGS. 4 a and 4 b. In block 318, fill factor values are identified,for the above determined parameters, that have approximately a 1/3 ratiobetween the difference of the effective refractive index fors-polarization and p-polarization. In block 320, a height of the gratingis determined for each instance having a 1/3 ratio between thedifference of the effective refractive index for s-polarization andp-polarization. In block 322, the height and fill factor are used todetermine the aspect ratio of the grating for each instance having a 1/3ratio between the difference of the effective refractive index fors-polarization and p-polarization. In block 324, the grating may befabricated, for example by etching, based on the parameters determinedin the above noted steps. In one embodiment, the fill factor with thesmallest height is selected. In another embodiment, the fill factor withthe lowest aspect ratio is selected.

The methodology of designing a p-polarized and s-polarized −1st orderdiffraction grating, may be accomplished by extending equations (1)-(4).Since the relationship between p-polarizations and s-polarizations isconsidered, a more general expression is introduced. When gratingheight, h_(p), for p-polarization or h_(s) for s-polarization satisfies(5), each polarization enhances diffraction efficiency of the −1storder.

$\begin{matrix}{{\left( {n_{d,p},n_{d,s}} \right) = \left( {\frac{\left( {{2i} - 1} \right)\lambda}{2h_{p}},\frac{\left( {{2j} - 1} \right)\lambda}{2h_{s}}} \right)}\left( {{i = 1},2,\ldots\mspace{14mu},{j = 1},2,\ldots} \right)} & (5)\end{matrix}$The −1st order diffraction of p-polarization and s-polarizations issimultaneously enhanced when required each height has the same physicalheight, h, as is given byh=h _(p) =h _(s)  (6)The p-polarization and s-polarized −1st order condition is written withthe ratio of effective refractive index differences, n_(d,p), forp-polarization to n_(d,s) for s-polarization.

$\begin{matrix}{\frac{n_{d,p}}{n_{d,s}} = \frac{\left( {{2i} - 1} \right)}{\left( {{2j} - 1} \right)}} & (7)\end{matrix}$Then, the grating height, h, is determined by equations (5)-(7).

One element of this design methodology is that the expression of theratio n_(d,p)/n_(d,s) allows appropriate grating parameters to be foundeasily according to the variation of fill factor for p-polarizations ands-polarizations. In this design methodology, infinite numberedcombinations of (i,j) fulfill equation (7). In practice, an appropriatedimension of the grating may be effectively selected in view offabrication constraints.

Now referring to FIGS. 4 a and 4 b, the effective index difference isgraphed with respect to the variation of the fill factor. The fillfactor is the ratio (r) of the grating ridge width of fused silica tothe grating period (p). More specifically, line 412 of FIG. 4 a denotesthe relationship for s-polarization at θ_(in)=30° and line 414 of FIG. 4a denotes the relationship for p-polarization at θ_(in)=30°. Meanwhile,line 422 of FIG. 4 b denotes the relationship for s-polarization atθ_(in)=50° and line 424 of FIG. 4 b denotes the relationship forp-polarization at θ_(in)=50°.

All points on the curves of p-polarization or s-polarization provide themaximum diffraction efficiency of the −1st order when the grating heightis set to fulfill equations (5). From the view point of fabrication, theminimum aspect ratio of the grating height to the edge width of fusedsilica or air may be desired. Although infinite numbered combinations(i,j) may satisfy equation (7), the two combinations, (i,j)=(1,1) and(1,3) are considered here. Those correspond to n_(d,p)/n_(d,s)=1 and1/3.

It can be seen in FIG. 4 a that n_(d,p)/n_(d,s) has a value of 1 atr=0.64 and 1/3 at r=0.21. On the other hand, n_(d,p/)n_(d,s) has 1 atr=0.93 and 1/3 at r=0.04 and 0.54 as shown in FIG. 4 b. Since there arethe two values of r for n_(d,p)/n_(d,s)=1/3, the ratios are respectivelynumbered as 1/3a and 1/3b. However, in reviewing FIGS. 4 a and 4 b notonly n_(d,p)/n_(d,s)=1 but also n_(d,p)/n_(d,s)=1/3 should be consideredto obtain the lower grating height in both p-polarizations ands-polarizations case, depending on an incident angle in Littrowmounting.

Effective refractive index differences fulfilling n_(d,p)/n_(d,s)=1 and3 were calculated in θ_(in) from 30° to 85° and plotted in FIG. 5 a.More specifically, line 512 is the effective index difference relativeto the incident angle θ_(in) for p-polarization in a first instance (a)where the ratio of the effective refractive index difference is about1/3. Line 514 is the effective index difference relative to the incidentangle θ_(in) for s-polarization in the first instance (a) where theratio of the effective refractive index difference is about 1/3.Similarly, line 516 is the effective index difference relative to theincident angle θ_(in) for p-polarization and line 518 is the effectiveindex difference relative to the incident angle θ_(in) fors-polarization in a second instance (b) where the ratio of the effectiverefractive index difference is about 1/3. Finally, line 520 is theeffective index difference relative to the incident angle θ_(in) forboth s and p-polarizations for the instance where the ratio of theeffective refractive index difference is 1.

The angular step width was basically 5° and further more angles wereadded at discontinuity points. It can be seen by line 520 that n_(d,p)and n_(d,s) exist within θ_(in) from 30° to 58° for the ratio of unity.On the other hand, in case of n_(d,p)/n_(d,s)=1/3, n_(d,p) and n_(d,s)have a first set numbered by 1/3a, in θ_(in) from 30° to 48.5°, and twosets by 1/3a and b, with the further increase of θ_(in).

The grating height was calculated from FIG. 5 a, using equation (5), andis presented in FIG. 5 b. As such, line 532 is the height relative tothe incident angle θ_(in), in the first instance (a) where the ratio ofthe effective refractive index difference is about 1/3. Line 534 is theheight relative to the incident angle θ_(in) in the second instance (b)where the ratio of the effective refractive index difference is about1/3. Finally, line 536 is the height relative to the incident angleθ_(in) where the ratio of the effective refractive index difference is1.

As illustrated, the grating height increases sharply forn_(d,p)/n_(d,s)=1 when increasing θ_(in) beyond 30°. Alternatively,n_(d,p)/n_(d,s)=1/3 provides a lower height than n_(d,p)/n_(d,s)=1 whenθ_(in) is larger than 43° with the further increase of θ_(in).

Accordingly, FIG. 5 c illustrates the corresponding fill factor for eachscenario. Line 552 denotes the value of the fill factor for each angleθ_(in) in the first instance (a) where the ratio of the effectiverefractive index difference is about 1/3. Line 554 denotes the value ofthe fill factor b for each angle θ_(in) in the second instance (b) wherethe ratio of the effective refractive index difference is about 1/3.Line 556 denotes the value of the fill factor for n_(d,p)/n_(d,s)=1 ateach angle θ_(in). The fill factors for n_(d,p)/n_(d,s)=1, 1/3 a, and1/3 b all increase with the increase of θ_(in).

In view of fabrication, the aspect ratio of the grating height to theedge width of fused silica or groove is taken to be smaller of the fusedsilica or groove width. The aspect ratio, AP_(opt), is given by

$\begin{matrix}{{AS}_{opt} - {\min\limits_{l}\left( {\max\left( {\frac{h_{l}}{r_{l}\lambda},\frac{h_{l}}{\left( {1 - r_{l}} \right)\lambda}} \right)} \right)}} & (8)\end{matrix}$where h_(l) and r_(l) are the grating height and fill factor thatfulfill equations (5)-(7). When the fill factor is less than 0.5, theedge width of fused silica is used, and when the fill factor is greaterthan 0.5 the groove width is selected. In FIGS. 5 a-5 c, the gratingparameters of the three cases, n_(d,p)/n_(d,s)=1, 1/3 a, and 1/3 b, arepresented. Similarly, FIG. 5 d illustrates the aspect ratio AP_(opt)with respect to the variation of θ_(in), as denoted by line 560. Thecondition n_(d,p)/n_(d,s)=1 provides the lowest aspect ratio of gratingwith the groove width of air less than 0.5 from 30° to 37.5° that arerepresent by n_(d,p)/n_(d,s)=1 and Air at the top of FIG. 5 d. Thecondition n_(d,p)/n_(d,s)=1/3 provides the lowest aspect ratio with thefurther increase of θ_(in), where the fill factor exceeds 0.5 at 47.5°.Then, n_(d,p)/n_(d,s) switches from 1/3, a, to 1/3, b at 60.2°. One veryinteresting and unexpected feature is that n_(d,p)/n_(d,s)=1/3 providesthe lowest aspect ratio when θ_(in) is larger than 37.5°, notn_(d,p)/n_(d,s)=1.

FIGS. 6 a and 6 b illustrate the diffraction efficiency with respect toa variation in height. In FIG. 6 a, the incident angle θ_(in)=30°, whilethe period p=λ, the fill factor r=0.64, and the height h=2.33λ. Line 612is the s-polarization diffraction efficiency to the −1^(st) order, whileline 614 is the s-polarization diffraction efficiency to the 0^(th)order. Line 616 is the p-polarization diffraction efficiency to the−1^(st) order, while line 618 is the p-polarization diffractionefficiency to the 0^(th) order.

In FIG. 6 b, the incident angle is θ_(in)=50°, while the periodp=0.653λ, the fill factor r=0.54, and the height h=4.44λ. Line 622 isthe s-polarization diffraction efficiency to the −1^(st) order, whileline 624 is the s-polarization diffraction efficiency to the 0^(th)order. Line 626 is the p-polarization diffraction efficiency to the−1^(st) order, while line 628 is the p-polarization diffractionefficiency to the 0^(th) order. The grating parameters are consistentwith FIG. 5 d.

For the instance where θ_(in)=30° in FIG. 6 a, the p-polarization ands-polarization have the same period with variation of height due ton_(d,p)/n_(d,s)32 1. Diffraction efficiency of −1st order is 94.9% forp-polarization and 96.2% for s-polarization at h=2.33λ. On the otherhand, the period with variation of height for s-polarization is onethird of that for p-polarization with n_(d,p)/n_(d,s)=1/3, whenθ_(in)=50° in FIG. 6 b. Diffraction efficiency is 90% for p-polarizationand 95.8% for s-polarization at h=4.44λ.

Consistent with this method other specific implementations may beparticularly useful. In one embodiment, the incident angle θ_(in) isabout 40° and the alternating ridges and grooves have a grating periodp=0.75λ-0.81λ, a fill factor r=0.32-0.42, a grating height h=4.1λ-4.7λ.In another embodiment, the incident angle θ_(in) is about 50° and thealternating ridges and grooves have a grating period p=0.62λ-0.68λ, afill factor r=0.49-0.59, a grating height h=4.1λ-4.7λ. In anotherembodiment, the incident angle θ_(in) is about 60° and the alternatingridges and grooves have a grating period p=0.55λ-0.61λ, a fill factorr=0.63-0.73, a grating height h=5.1λ-5.7λ. In yet another embodiment,the incident angle θ_(in) is about 70° and the alternating ridges andgrooves have a grating period p=0.5λ-0.56λ, a fill factor r=0.34-0.44, agrating height h=2.8λ-3.4λ.

FIG. 7 illustrates the best diffraction efficiency to the −1^(st) orderfor each of conditions discussed with respect to the variation ofincident angle. Line 712 denotes the diffraction efficiency fors-polarization and line 714 denotes the diffraction efficiency forp-polarization. The grating parameters are consistent with FIG. 5 d.Further, the angular step width was calculated at 5° steps and furthermore angles were added at discontinuity points. Diffraction efficiencyis higher than 90% for p-polarization and 92.5% for s-polarization from30° to 50°, and 79.2% and 87.9% with a further increase up to 65°.

One application based on the design methodology is presented in FIG. 8.A light assembly 810, for example as a tail or brake light for avehicle, comprises a light source 812 and a grating 814. The lightsource 812 may be comprised of unpolarized lights such as light emittingdiodes. Light generated from the light source 812 is denoted by arrow820. Further, the light 820 includes an s-polarization component and ap-polarization component. The grating 814 may have all of the featuresdescribed above with respect to the grating 11 and resulting from theprocesses herein described. As such, the light may be directed at thegrating with an incident angle of between 40° and 70° degrees, forexample at approximately 55.4°. According to one embodiment, the gratingmay couple the light at a 90° angle to direct the light out fromvehicle, for example through a lens 816.

Light that travels through two different media, such as air and silica,has a bend angle of |θ_(in)−θ_(r,0)|, and the angle is generally largerthan 90° when the 0^(th) order diffraction is used. On the other hand,the −1st order diffraction has the light bend angle of θ_(in)+θ_(r,−1),and can provide a light bend angle less than 90°. Thus, a 90° couplercould be built to direct light without additional materials rather thanusing a traditional 45° inclined mirror. Unpolarized light is directedupon the grating with an incident angle of 55.4°. When the grating isdesigned according the methodology described, it redirects to thetransmitted light to the −1^(st) order mode with an angle of 34.6°,resulting in a 90° bend of the light.

Potential ranges for the incident angle and wavelength of a 90° couplerare shown in FIGS. 9 a and 9 b. In FIG. 9 a, line 912 corresponds to thes-polarization diffraction efficiency for the −1st order and line 914corresponds to the s-polarization diffraction efficiency for the 0^(th)order with respect to the change in incident angle θ_(in). Line 916corresponds to the p-polarization diffraction efficiency for the −1^(st)order and line 918 corresponds to the p-polarization diffractionefficiency for the 0^(th) order with respect to the change in incidentangle θ_(in).

FIG. 9 a illustrates that the wavelength bandwidths of s-polarizationare wider than those of p-polarization. This is due to the fact that theeffective refractive index difference for s-polarization is larger thanthat for p-polarization in the grating. In FIG. 9 b, line 922 is thes-polarization diffraction efficiency for the −1^(st) order and line 924is the s-polarization diffraction efficiency for the 0^(th) order withrespect to the normalized wavelength variation λ. Line 926 is thep-polarization diffraction efficiency for the −1^(st) order and line 928is the p-polarization diffraction efficiency for the 0^(th) order withrespect to the normalized wavelength variation λ.

As such, the angular bandwidth for a transmittance larger than 50% is9.40 for p-polarization and 18.60 for s-polarization. Wavelengthbandwidth for a transmittance larger than 50% is 0.088λ forp-polarization and 0.212λ for s-polarization.

As a person skilled in the art will readily appreciate, the abovedescription is meant as an illustration of the principles thisapplication. This description is not intended to limit the scope orapplication of the invention in that the invention is susceptible tomodification, variation and change, without departing from spirit of theinvention, as defined in the following claims.

1. A grating structure comprised of a base, the base having alternatingridges and grooves forming a grating, the grating having a ratio betweenthe effective refractive index difference between s-polarization andp-polarization of about 1/3 thereby directing both s-polarization andp-polarization components of incident light to the −1^(st) orderdiffraction mode, where the incident light has an incident angle θ_(in)of between 40° and 90° and a wavelength λ=350-1600 nm.
 2. The gratingstructure according to claim 1, wherein the grating is in a Littrowmounting condition, such that a −1^(st) order diffraction mode has afirst diffraction angle and a 0^(th) order diffraction mode has a seconddiffraction angle, wherein the first diffraction angle is equal to thesecond diffraction angle.
 3. The grating structure according to claim 1,wherein the −1st order diffraction mode has a diffraction angle that isabout 90 degrees relative to the incident angle.
 4. The gratingstructure according to claim 1, wherein the base is a fused silica baseand the ridges and grooves form a fused silica to air interface.
 5. Thegrating structure according to claim 4, wherein the incident angleθ_(in) is about 40° and the alternating ridges and grooves have agrating period p=0.75λ-0.81λ, a fill factor r=0.32-0.42, a gratingheight h=4.1λ-4.7λ.
 6. The grating structure according to claim 4,wherein the incident angle θ_(in) is about 50° and the alternatingridges and grooves have a grating period p=0.62λ-0.68λ, a fill factorr=0.49-0.59, a grating height h=4.1λ-4.7λ.
 7. The grating structureaccording to claim 4, wherein the incident angle θ_(in) is about 60° andthe alternating ridges and grooves have a grating period p=0.55λ-0.61λ,a fill factor r=0.63-0.73, a grating height h=5.1λ-5.7λ.
 8. The gratingstructure according to claim 4, wherein the incident angle θ_(in) isabout 70° and the alternating ridges and grooves have a grating periodp=0.5λ-0.56λ, a fill factor r=0.34-0.44, a grating height h=2.8λ-3.4λ.9. A light assembly for a vehicle comprising: a non-polarized lightsource that generates rays of light; a grating having a base, the basehaving alternating ridges and grooves, the grating having a ratiobetween the effective refractive index difference between s-polarizationand p-polarization of about 1/3 thereby directing both s-polarizationand p-polarization components of the light to the −1^(st) orderdiffraction mode, where the light has an incident angle θ_(in) ofbetween 40° and 70° and a wavelength λ=350-1600 nm.
 10. The lightassembly according to claim 9, wherein the grating is in a Littrowmounting condition, such that a −1^(st) order diffraction mode has afirst diffraction angle and a 0^(th) order diffraction mode has a seconddiffraction angle, wherein the first diffraction angle is equal to thesecond diffraction angle.
 11. The light assembly according to claim 9,wherein the −1^(st) order diffraction mode has a diffraction angle thatis about 90 degrees relative to the incident angle.
 12. The lightassembly according to claim 9, wherein the base is a fused silica baseand the ridges and grooves form a fused silica to air interface.
 13. Thelight assembly according to claim 12, wherein the incident angle θ_(in)is about 40° and the alternating ridges and grooves have a gratingperiod p=0.75λ-0.81λ, a fill factor r=0.32-0.42, a grating heighth=4.1λ-4.7λ.
 14. The light assembly according to claim 12, wherein theincident angle θ_(in) is about 50° and the alternating ridges andgrooves have a grating period p=0.62λ-0.68λ, a fill factor r=0.49-0.59,a grating height h=4.1λ-4.7λ.
 15. The light assembly according to claim12, wherein the incident angle θ_(in) is about 60° and the alternatingridges and grooves have a grating period p=0.55λ-0.61λ, a fill factorr=0.63-0.73, a grating height h=5.1λ-5.7λ.
 16. The light assemblyaccording to claim 12, wherein the incident angle θ_(in) is about 70°and the alternating ridges and grooves have a grating periodp=0.5λ-0.56λ, a fill factor r=0.34-0.44, a grating height h=2.8λ-3.4λ.17. A method of coupling an unpolarized light beam comprising: providinga grating with a ratio of the effective refractive index differencebetween s-polarization and p-polarization of about 1/3; providing anunpolarized light beam at an incident angle between about 40° and 90°;diffracting the unpolarized light beam such that p-polarizationcomponents and s-polarization components of incident light are directedto the −1^(st) order diffraction mode.
 18. The method according to claim17, wherein the grating is in a Littrow mounting condition.
 19. Themethod according to claim 17, wherein the −1^(st) order diffraction modehas a diffraction angle that is about 90 degrees relative to theincident angle.